Two similar triangles ABC and A1B1C1 are given. Find the coefficient of similarity

Two similar triangles ABC and A1B1C1 are given. Find the coefficient of similarity if S ABC = 25cm2 and S A1B1C1 = 81cm2.

The coefficient of similarity is the ratio of any corresponding linear dimensions of the first figure to the linear dimensions of the second figure, located opposite the same angles.
And since the area of the triangle is equal to the product of the sides AB, BC, and the sine of the angle between them, and A1B1 = k * AB, B1C1 = k * BC, to the coefficient of similarity, then:
S A1B1C1 = A1B1 * B1C1 * sin <(A1B1, B1C1) = 81 (cm2) = k * AB * k * BC * sin <(AB, BC) = k ^ 2 * S ABC
S ABC = AB * BC * sin <(AB, BC) = 25 (cm2).
k ^ 2 = S A1B1C1 / S ABC = 81/25, k = 9/5 = 1.8